Nacim Ramdani

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In this paper, we show how to compute an over-approximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on state-of-the-art validated numerical integration(More)
This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary di"erential equation(More)
We investigate solution techniques for numerical constraint satisfaction problems and validated numerical set integration methods for computing reachable sets of nonlinear hybrid dynamical systems in presence of uncertainty. To use interval simulation tools with higher dimensional hybrid systems, while assuming large domains for either initial continuous(More)
In this paper, we investigate nonlinear reachability computation in presence of model uncertainty, via guaranteed set integration. We show how this can be done by using the classical Müller’s existence theorem. The core idea developed is to no longer deal with whole sets but to derive instead two nonlinear dynamical systems which involve no model(More)
This paper models recent data in the field of postural coordination showing the existence of self-organized postural states, and transition between them, underlying supra-postural tracking movements. The proposed closed-loop controller captures the complex postural behaviors observed in humans and can be used to implement efficient and simple balance(More)
Computing the reachable set of hybrid dynamical systems in a reliable and verified way is an important step when addressing verification or synthesis tasks. This issue is still challenging for uncertain nonlinear hybrid dynamical systems. We show in this paper how to combine a method for computing continuous transitions via interval Taylor methods and a(More)
For many thermal processes described by partial differential equations, parametric identification of the model can be performed by solving an inverse problem. Measurements noises occurring on one or several measured characteristic states have to be carefully taken into account in order to provide robust identification procedures. However, spatial inaccuracy(More)
This paper presents a contribution for restoring standing in paraplegia while using functional electrical stimulation (FES). Movement generation induced by FES remains mostly open looped and stimulus intensities are tuned empirically. To design an efficient closed-loop control, a preliminary study has been carried out to investigate the relationship between(More)